# golay.ancillaPrep.py :
#
# This is a list of 100 random Golay |0>_L encoding circuits, created with 
#  '2010-01-21 Golay ancilla preparation.nb'.
# The format is [[[control1,target1],... in round one],[same for round two],...,[same for round seven]].
# 
# Ben Reichardt, 1/23/2010
#
# Here are some of the pairs of encoding circuits (specified by their indices in the list below, 
# and also a permutation of the seven rounds) that work well for verification against X errors.
# Note that some of them are fully fault-tolerant against X errors!  A few are also just permutations 
# of the same preparation circuit (e.g., 11 11 below), which is nice.
# 0 21 [2, 6, 3, 0, 5, 1, 4] [6, 0, 5, 4, 1, 3, 2] 1 X (16)
# 5 25 [5, 6, 2, 4, 0, 1, 3] [0, 5, 3, 4, 1, 6, 2] 1 X (80)
# 6 17 [0, 6, 1, 3, 4, 2, 5] [3, 6, 0, 1, 2, 4, 5] 1 X (15)
# 11 11 [4, 6, 5, 3, 1, 2, 0] [0, 6, 1, 2, 4, 3, 5] 1 X (6) !
# 13 46 [4, 3, 0, 5, 6, 2, 1] [2, 0, 4, 1, 6, 5, 3] 1 X (83)
# 17 48 [6, 4, 0, 5, 1, 2, 3] [6, 2, 3, 1, 4, 0, 5] 1 X (33)
# 19 27 [0, 6, 2, 4, 5, 3, 1] [5, 6, 4, 0, 3, 2, 1] 1 X (12)
# 19 44 [2, 0, 6, 1, 5, 4, 3] [5, 0, 6, 3, 2, 4, 1] 1 X (82)
# 29 47 [6, 5, 4, 2, 3, 1, 0] [2, 3, 5, 4, 1, 0, 6] 1 X (90)
# 36 42 [2, 3, 0, 6, 5, 4, 1] [1, 4, 5, 2, 6, 0, 3] 1 X (7)
# 41 41 [0, 1, 3, 6, 4, 5, 2] [5, 6, 2, 1, 4, 3, 0] 1 X (70) !
# 42 45 [3, 4, 1, 6, 0, 5, 2] [4, 6, 1, 3, 2, 5, 0] 1 X (78)
# 44 48 [1, 0, 4, 2, 6, 3, 5] [0, 5, 4, 1, 6, 2, 3] 1 X (54)
# 45 49 [4, 5, 2, 1, 6, 0, 3] [2, 5, 3, 6, 0, 4, 1] 1 X (77)
# It might be worth running these pairs again in case a slightly different permutation works perfectly.
# For the following good results, I had the code do another 100 trials if a 1 X was found: 
# 0 81 [0, 4, 5, 1, 6, 2, 3] [4, 6, 0, 3, 1, 5, 2] 1 X (75)
# 0 93 [5, 2, 0, 1, 3, 4, 6] [5, 6, 0, 1, 4, 2, 3] 0 X (7) !!!!!!!
# 1 16 [5, 2, 1, 4, 0, 3, 6] [6, 3, 5, 2, 1, 0, 4] 1 X (83)
# 1 16 [4, 3, 1, 0, 5, 6, 2] [1, 5, 3, 0, 2, 4, 6] 1 X (86)
# 1 41 [5, 3, 4, 2, 1, 0, 6] [1, 3, 0, 6, 5, 2, 4] 1 X (57)
# 2 3 [1, 4, 5, 0, 6, 3, 2] [3, 5, 4, 1, 6, 2, 0] 1 X (5)
# 2 96 [6, 4, 1, 5, 3, 2, 0] [3, 5, 0, 2, 1, 6, 4] 1 X (38)
# 3 3 [6, 0, 2, 5, 4, 1, 3] [1, 4, 6, 2, 3, 0, 5] 1 X (51) !
# 3 9 [5, 0, 6, 3, 2, 4, 1] [5, 2, 3, 0, 6, 4, 1] 1 X (70)
# 3 9 [0, 4, 5, 2, 3, 1, 6] [6, 5, 1, 0, 2, 3, 4] 1 X (74)
# 3 54 [2, 0, 5, 6, 3, 4, 1] [5, 4, 1, 0, 2, 6, 3] 1 X (44)
# 4 75 [6, 4, 3, 2, 1, 5, 0] [6, 5, 1, 3, 2, 0, 4] 1 X (60)
# 4 87 [6, 5, 1, 3, 0, 2, 4] [6, 3, 5, 2, 1, 4, 0] 1 X (53)
# 5 50 [2, 6, 1, 4, 0, 3, 5] [2, 6, 1, 3, 4, 0, 5] 1 X (87)
# 5 75 [4, 1, 0, 6, 5, 3, 2] [0, 2, 3, 5, 6, 1, 4] 1 X (77)
# 6 41 [2, 5, 0, 4, 1, 6, 3] [0, 3, 4, 6, 5, 2, 1] 1 X (53)
# 6 54 [2, 5, 6, 4, 3, 0, 1] [1, 6, 3, 5, 2, 0, 4] 1 X (35)
# 6 56 [5, 1, 0, 6, 3, 4, 2] [0, 6, 1, 3, 4, 2, 5] 1 X (2)
# 6 91 [5, 3, 0, 6, 2, 4, 1] [2, 0, 3, 6, 1, 5, 4] 1 X (55)
# 6 96 [3, 1, 5, 0, 4, 2, 6] [5, 0, 2, 4, 3, 1, 6] 1 X (52)
# 7 71 [0, 5, 3, 4, 2, 1, 6] [1, 0, 5, 3, 4, 2, 6] 1 X (30)
# 7 73 [5, 2, 0, 1, 3, 4, 6] [4, 5, 3, 2, 6, 0, 1] 1 X (72)
# 7 80 [1, 2, 4, 6, 3, 5, 0] [6, 4, 5, 2, 3, 1, 0] 1 X (1)
# 7 80 [0, 5, 4, 2, 3, 1, 6] [5, 2, 3, 6, 1, 0, 4] 1 X (18)
# 7 80 [0, 2, 6, 4, 5, 1, 3] [1, 6, 4, 5, 2, 0, 3] 1 X (6)
# 7 80 [2, 0, 3, 1, 5, 4, 6] [1, 3, 2, 0, 4, 5, 6] 1 X (17)
# 8 17 [1, 5, 4, 0, 6, 2, 3] [2, 0, 3, 5, 6, 1, 4] 1 X (9)
# 8 36 [6, 1, 0, 2, 5, 4, 3] [4, 0, 6, 3, 2, 5, 1] 1 X (63)
# 8 70 [0, 6, 2, 4, 1, 3, 5] [1, 4, 5, 6, 0, 3, 2] 0 X (8) !!!!!!!
# 9 20 [2, 0, 5, 3, 6, 4, 1] [0, 5, 2, 1, 3, 6, 4] 1 X (50)
# 9 22 [4, 6, 2, 1, 0, 5, 3] [1, 4, 0, 2, 6, 5, 3] 1 X (20)
# 9 30 [3, 0, 6, 4, 5, 1, 2] [0, 4, 3, 1, 2, 6, 5] 1 X (46)
# 9 48 [1, 3, 0, 5, 2, 6, 4] [5, 2, 6, 3, 0, 4, 1] 1 X (31)
# 9 63 [2, 3, 4, 5, 6, 0, 1] [4, 0, 5, 6, 2, 1, 3] 1 X (77)
# 10 15 [3, 2, 5, 4, 1, 6, 0] [4, 5, 0, 6, 2, 3, 1] 1 X (77)
# 10 65 [6, 1, 0, 3, 4, 2, 5] [0, 4, 2, 6, 1, 5, 3] 1 X (6)
# 11 26 [3, 6, 0, 1, 4, 2, 5] [6, 0, 5, 1, 3, 2, 4] 0 X (43) !!!!!!!
# 12 15 [4, 0, 6, 1, 5, 2, 3] [3, 4, 2, 1, 0, 6, 5] 1 X (31)
# 12 63 [5, 4, 3, 6, 1, 2, 0] [0, 6, 5, 3, 4, 1, 2] 1 X (1)
# 12 80 [0, 3, 6, 1, 5, 4, 2] [1, 3, 0, 4, 5, 2, 6] 1 X (69)
# 12 86 [2, 1, 5, 4, 6, 3, 0] [0, 3, 1, 4, 5, 6, 2] 1 X (53)
# 13 21 [6, 1, 0, 4, 5, 2, 3] [6, 3, 4, 1, 5, 0, 2] 1 X (3)
# 13 57 [3, 0, 6, 2, 5, 4, 1] [5, 2, 1, 4, 6, 0, 3] 1 X (70)
# 14 53 [1, 3, 0, 5, 6, 2, 4] [5, 1, 2, 6, 3, 0, 4] 1 X (15)
# 14 59 [2, 4, 6, 0, 1, 3, 5] [2, 6, 3, 4, 5, 0, 1] 1 X (27)
# 14 59 [6, 4, 2, 0, 5, 1, 3] [6, 2, 3, 4, 5, 0, 1] 1 X (15)
# 14 76 [1, 5, 2, 6, 4, 0, 3] [3, 4, 2, 1, 5, 6, 0] 1 X (57)
# 15 75 [1, 2, 3, 6, 4, 5, 0] [6, 0, 3, 1, 5, 2, 4] 1 X (6)
# 16 34 [4, 5, 0, 2, 1, 3, 6] [5, 1, 3, 4, 0, 2, 6] 1 X (16)
# 16 87 [2, 3, 1, 0, 6, 5, 4] [1, 2, 0, 5, 3, 6, 4] 1 X (23)
# 16 88 [0, 4, 2, 3, 5, 1, 6] [5, 0, 3, 6, 4, 2, 1] 1 X (6)
# 17 47 [0, 3, 2, 5, 6, 1, 4] [1, 0, 3, 2, 4, 5, 6] 1 X (52)
# 17 76 [4, 6, 2, 0, 5, 3, 1] [0, 2, 1, 6, 5, 4, 3] 1 X (93)
# 17 92 [0, 3, 5, 6, 4, 2, 1] [5, 3, 0, 2, 1, 6, 4] 1 X (55)
# 18 25 [6, 3, 4, 0, 1, 5, 2] [3, 6, 1, 0, 4, 2, 5] 1 X (56)
# 19 50 [4, 3, 6, 2, 5, 0, 1] [0, 2, 3, 6, 5, 4, 1] 1 X (1)
# 20 58 [4, 5, 0, 6, 1, 2, 3] [4, 0, 5, 2, 6, 3, 1] 1 X (43)
# 20 73 [3, 6, 4, 0, 2, 1, 5] [2, 6, 3, 4, 0, 1, 5] 1 X (25)
# 20 73 [6, 2, 3, 5, 0, 1, 4] [5, 3, 4, 0, 2, 1, 6] 1 X (23)
# 21 30 [1, 5, 3, 2, 4, 6, 0] [2, 0, 1, 5, 3, 6, 4] 1 X (37)
# 21 47 [3, 6, 4, 0, 5, 1, 2] [6, 5, 3, 2, 4, 0, 1] 1 X (38)
# 21 76 [0, 2, 1, 6, 5, 4, 3] [1, 6, 5, 3, 0, 2, 4] 1 X (70)
# 21 81 [0, 5, 4, 1, 3, 6, 2] [3, 1, 2, 0, 6, 5, 4] 1 X (16)
# 23 94 [5, 3, 1, 2, 6, 0, 4] [6, 3, 5, 4, 2, 0, 1] 1 X (64)
# 23 98 [2, 1, 4, 3, 6, 5, 0] [4, 5, 6, 0, 2, 1, 3] 1 X (29)
# 24 87 [5, 4, 2, 0, 6, 3, 1] [0, 6, 1, 5, 2, 3, 4] 1 X (54)
# 26 30 [5, 1, 6, 4, 0, 2, 3] [1, 0, 5, 6, 4, 2, 3] 1 X (17)
# 26 52 [2, 5, 1, 3, 4, 0, 6] [5, 6, 4, 1, 3, 2, 0] 1 X (29)
# 27 32 [1, 0, 2, 4, 6, 3, 5] [3, 2, 1, 0, 5, 6, 4] 1 X (44)
# 29 33 [0, 4, 6, 1, 5, 3, 2] [1, 5, 0, 2, 3, 6, 4] 1 X (53)
# 29 44 [0, 5, 4, 6, 2, 3, 1] [3, 1, 0, 2, 5, 6, 4] 0 X (0) !!!!!!!
# 29 68 [2, 4, 6, 5, 1, 0, 3] [4, 1, 3, 5, 2, 0, 6] 1 X (11)
# 30 47 [1, 6, 3, 5, 2, 0, 4] [5, 2, 1, 0, 6, 3, 4] 1 X (58)
# 30 59 [2, 3, 5, 4, 6, 1, 0] [6, 2, 1, 4, 5, 3, 0] 1 X (92)
# 30 59 [4, 2, 3, 5, 6, 0, 1] [3, 2, 6, 1, 4, 0, 5] 0 X (80) !!!!!!!
# 31 77 [3, 1, 2, 0, 5, 4, 6] [2, 5, 4, 3, 1, 6, 0] 1 X (49)
# 31 89 [5, 1, 2, 4, 0, 3, 6] [3, 1, 5, 4, 0, 6, 2] 1 X (90)
# 33 87 [3, 1, 2, 0, 6, 4, 5] [0, 5, 2, 4, 1, 3, 6] 1 X (41)
# 34 68 [3, 4, 5, 6, 2, 0, 1] [4, 0, 2, 6, 3, 1, 5] 1 X (64)
# 34 79 [2, 4, 6, 1, 3, 0, 5] [3, 6, 1, 5, 0, 4, 2] 1 X (71)
# 34 87 [1, 5, 6, 3, 4, 0, 2] [2, 1, 0, 5, 3, 4, 6] 1 X (78)
# 35 39 [4, 3, 0, 2, 1, 6, 5] [4, 0, 2, 6, 3, 1, 5] 1 X (93)
# 35 46 [4, 6, 0, 3, 1, 2, 5] [0, 3, 6, 2, 4, 5, 1] 1 X (34)
# 35 47 [2, 1, 0, 3, 4, 6, 5] [5, 2, 6, 0, 4, 3, 1] 1 X (61)
# 35 55 [6, 2, 1, 5, 4, 3, 0] [0, 1, 3, 2, 5, 6, 4] 1 X (41)
# 35 60 [2, 4, 1, 5, 6, 3, 0] [6, 0, 5, 4, 3, 1, 2] 1 X (69)
# 36 53 [4, 2, 5, 1, 6, 3, 0] [1, 4, 5, 6, 2, 0, 3] 1 X (76)
# 36 54 [6, 3, 0, 1, 2, 5, 4] [4, 2, 3, 5, 6, 0, 1] 1 X (45)
# 37 84 [5, 1, 3, 0, 2, 4, 6] [1, 3, 6, 5, 2, 0, 4] 1 X (21)
# 38 87 [2, 5, 1, 3, 0, 6, 4] [4, 0, 5, 3, 2, 6, 1] 1 X (27)
# 39 51 [3, 6, 1, 2, 4, 0, 5] [5, 6, 4, 2, 3, 1, 0] 1 X (57)
# 40 43 [5, 2, 4, 3, 0, 1, 6] [4, 1, 2, 3, 5, 6, 0] 1 X (93)
# 40 78 [0, 5, 3, 1, 4, 2, 6] [1, 4, 2, 5, 3, 0, 6] 1 X (71)
# 44 50 [5, 6, 0, 2, 3, 1, 4] [5, 6, 4, 3, 0, 2, 1] 1 X (82)
# 44 68 [6, 4, 2, 0, 3, 5, 1] [2, 6, 4, 3, 5, 1, 0] 1 X (56)
# 44 68 [0, 1, 5, 4, 3, 6, 2] [5, 3, 0, 2, 1, 4, 6] 1 X (70)
# 44 95 [6, 0, 1, 5, 3, 2, 4] [6, 1, 4, 5, 0, 3, 2] 1 X (87)
# 45 99 [6, 5, 1, 3, 2, 4, 0] [0, 5, 1, 3, 6, 4, 2] 0 X (45) !!!!!!!
# 46 57 [6, 5, 0, 3, 4, 2, 1] [5, 2, 0, 4, 1, 3, 6] 1 X (69)
# 46 96 [5, 1, 2, 3, 4, 0, 6] [6, 4, 1, 5, 3, 0, 2] 1 X (24)
# 47 77 [6, 0, 2, 4, 1, 3, 5] [4, 6, 2, 5, 3, 1, 0] 1 X (77)
# 48 58 [2, 0, 4, 1, 3, 5, 6] [1, 6, 4, 2, 3, 5, 0] 1 X (88)
# 49 88 [1, 5, 0, 2, 4, 3, 6] [1, 3, 0, 2, 5, 4, 6] 1 X (38)
# 50 62 [5, 1, 2, 0, 4, 6, 3] [4, 2, 5, 1, 0, 6, 3] 1 X (77)
# 50 68 [4, 5, 2, 0, 1, 3, 6] [3, 4, 5, 6, 0, 2, 1] 1 X (54)
# 50 97 [4, 6, 5, 2, 1, 0, 3] [3, 0, 6, 4, 2, 1, 5] 1 X (65)
# 52 89 [0, 4, 3, 6, 1, 2, 5] [3, 2, 5, 4, 1, 6, 0] 0 X (58) !!!!!!!
# 54 61 [3, 4, 0, 1, 6, 5, 2] [4, 6, 3, 2, 5, 0, 1] 1 X (42)
# 54 73 [0, 6, 2, 1, 4, 5, 3] [0, 5, 2, 4, 6, 3, 1] 1 X (22)
# 54 97 [2, 3, 5, 0, 1, 4, 6] [1, 2, 3, 0, 6, 5, 4] 1 X (37)
# 54 99 [2, 3, 6, 4, 5, 0, 1] [6, 0, 1, 2, 3, 4, 5] 1 X (71)
# 55 69 [3, 4, 6, 5, 2, 1, 0] [5, 4, 0, 1, 3, 2, 6] 1 X (87)
# 56 67 [5, 0, 2, 4, 6, 3, 1] [0, 5, 1, 6, 2, 3, 4] 1 X (30)
# 57 60 [5, 3, 2, 4, 1, 0, 6] [0, 2, 4, 1, 6, 5, 3] 1 X (90)
# 57 84 [4, 5, 0, 3, 2, 6, 1] [1, 6, 3, 5, 2, 4, 0] 0 X (28) !!!!!!!
# 58 70 [3, 0, 1, 5, 6, 4, 2] [4, 0, 2, 3, 1, 6, 5] 1 X (41)
# 60 87 [4, 3, 1, 6, 5, 0, 2] [3, 2, 5, 1, 0, 4, 6] 1 X (27)
# 63 80 [3, 6, 0, 4, 1, 2, 5] [3, 0, 6, 5, 4, 1, 2] 0 X (58) !!!!!!!
# 63 88 [6, 1, 2, 4, 3, 0, 5] [3, 6, 4, 0, 2, 1, 5] 1 X (81)
# 65 86 [1, 2, 0, 3, 5, 4, 6] [0, 6, 5, 3, 4, 1, 2] 1 X (5)
# 67 71 [5, 4, 6, 2, 3, 0, 1] [1, 0, 3, 5, 4, 6, 2] 1 X (34)
# 71 87 [1, 0, 5, 4, 6, 3, 2] [3, 5, 2, 6, 0, 4, 1] 1 X (69)
# 74 92 [1, 0, 5, 6, 3, 4, 2] [2, 1, 3, 4, 6, 0, 5] 1 X (70)
# 76 99 [6, 2, 5, 0, 1, 4, 3] [2, 1, 6, 0, 3, 4, 5] 0 X (49) !!!!!!!
# 77 87 [1, 5, 0, 3, 4, 2, 6] [1, 2, 4, 3, 0, 6, 5] 1 X (37)
# 82 83 [2, 4, 3, 6, 0, 5, 1] [1, 0, 4, 6, 2, 5, 3] 1 X (77)
# 82 87 [4, 5, 0, 2, 6, 3, 1] [2, 3, 6, 1, 5, 0, 4] 1 X (72)
# 82 93 [4, 5, 6, 2, 0, 3, 1] [0, 2, 3, 1, 6, 5, 4] 1 X (4)
# 82 93 [4, 1, 5, 6, 3, 0, 2] [5, 3, 6, 4, 0, 2, 1] 1 X (36)
# 82 93 [0, 5, 2, 4, 3, 1, 6] [3, 5, 0, 4, 1, 2, 6] 1 X (88)
# 82 97 [0, 4, 5, 2, 1, 3, 6] [3, 0, 6, 2, 1, 4, 5] 1 X (29)
# 88 95 [6, 2, 5, 4, 0, 3, 1] [6, 2, 5, 1, 4, 3, 0] 1 X (7)
# 90 91 [3, 5, 2, 4, 0, 6, 1] [5, 6, 4, 1, 3, 0, 2] 0 X (45) !!!!!!!
# (I was running the code twice in parallel because my laptop has two CPU cores.)
#
from qfault.counting.location import Locations
from qfault.golay import overlap
from qfault.util.counterUtils import locXprep, locZprep, loccnot, locrest, \
	propagateAllErrors
from warnings import warn

preparationCircuits = [[[[1,0],[5,14],[9,20],[10,4],[11,19],[12,2],[13,7],[15,6],[17,16],[18,8],[21,3]],[[1,2],[5,6],[9,14],[10,22],[11,7],[12,20],[13,16],[15,19],[17,8],[18,3],[21,0]],[[1,4],[5,0],[9,19],[10,6],[11,2],[12,22],[13,20],[15,3],[17,7],[18,16],[21,8]],[[1,6],[5,2],[9,0],[10,16],[11,8],[12,4],[13,3],[15,20],[17,19],[18,14],[21,22]],[[1,8],[5,19],[9,7],[10,3],[11,0],[12,16],[13,4],[15,14],[17,2],[18,22],[21,20]],[[1,14],[5,16],[9,2],[10,8],[11,22],[12,7],[13,0],[15,4],[17,20],[18,19],[21,6]],[[1,20],[5,22],[9,3],[10,2],[11,4],[12,14],[13,8],[15,16],[17,6],[18,7],[21,19]]],
[[[0,4],[1,22],[7,9],[10,6],[11,2],[12,13],[14,3],[15,18],[17,8],[19,21],[20,16]],[[0,5],[1,9],[7,13],[10,2],[11,22],[12,21],[14,8],[15,16],[17,18],[19,6],[20,4]],[[0,6],[1,13],[7,22],[10,3],[11,21],[12,8],[14,4],[15,9],[17,5],[19,16],[20,18]],[[0,8],[1,3],[7,2],[10,22],[11,4],[12,18],[14,21],[15,5],[17,16],[19,9],[20,13]],[[0,9],[1,21],[7,18],[10,8],[11,16],[12,2],[14,13],[15,4],[17,6],[19,3],[20,5]],[[0,13],[1,8],[7,4],[10,16],[11,5],[12,9],[14,18],[15,3],[17,22],[19,2],[20,6]],[[0,22],[1,16],[7,3],[10,4],[11,9],[12,5],[14,6],[15,8],[17,21],[19,18],[20,2]]],
[[[0,7],[1,18],[3,16],[4,11],[6,8],[10,19],[13,12],[14,5],[20,2],[21,9],[22,17]],[[0,8],[1,19],[3,12],[4,15],[6,17],[10,18],[13,2],[14,16],[20,9],[21,5],[22,11]],[[0,11],[1,17],[3,9],[4,2],[6,15],[10,16],[13,8],[14,7],[20,5],[21,19],[22,12]],[[0,15],[1,9],[3,8],[4,7],[6,5],[10,11],[13,19],[14,17],[20,12],[21,18],[22,16]],[[0,16],[1,8],[3,7],[4,5],[6,12],[10,2],[13,17],[14,18],[20,15],[21,11],[22,19]],[[0,17],[1,12],[3,2],[4,18],[6,7],[10,8],[13,11],[14,9],[20,16],[21,15],[22,5]],[[0,18],[1,16],[3,11],[4,12],[6,9],[10,5],[13,15],[14,2],[20,19],[21,17],[22,7]]],
[[[0,1],[3,12],[4,6],[8,19],[9,2],[10,7],[11,14],[13,20],[17,16],[18,15],[22,21]],[[0,5],[3,20],[4,1],[8,14],[9,19],[10,16],[11,15],[13,21],[17,12],[18,7],[22,2]],[[0,14],[3,21],[4,12],[8,7],[9,20],[10,6],[11,16],[13,2],[17,5],[18,19],[22,1]],[[0,15],[3,19],[4,7],[8,1],[9,16],[10,21],[11,2],[13,12],[17,14],[18,5],[22,6]],[[0,19],[3,7],[4,14],[8,12],[9,15],[10,5],[11,21],[13,6],[17,20],[18,1],[22,16]],[[0,20],[3,1],[4,21],[8,2],[9,5],[10,12],[11,7],[13,19],[17,6],[18,16],[22,15]],[[0,21],[3,16],[4,15],[8,5],[9,12],[10,2],[11,19],[13,14],[17,1],[18,6],[22,20]]],
[[[0,1],[3,15],[4,14],[6,5],[7,13],[9,18],[12,16],[19,8],[20,2],[21,10],[22,17]],[[0,5],[3,10],[4,1],[6,14],[7,15],[9,11],[12,13],[19,18],[20,17],[21,8],[22,16]],[[0,8],[3,16],[4,5],[6,10],[7,11],[9,13],[12,17],[19,2],[20,1],[21,18],[22,14]],[[0,13],[3,8],[4,15],[6,17],[7,5],[9,16],[12,10],[19,11],[20,18],[21,1],[22,2]],[[0,14],[3,11],[4,16],[6,8],[7,17],[9,2],[12,15],[19,10],[20,5],[21,13],[22,1]],[[0,16],[3,14],[4,2],[6,13],[7,1],[9,15],[12,18],[19,5],[20,8],[21,17],[22,11]],[[0,18],[3,13],[4,10],[6,2],[7,14],[9,1],[12,5],[19,16],[20,15],[21,11],[22,8]]],
[[[1,3],[5,2],[11,6],[12,8],[14,4],[15,9],[17,0],[18,10],[20,7],[21,13],[22,16]],[[1,4],[5,16],[11,3],[12,6],[14,19],[15,7],[17,2],[18,13],[20,0],[21,8],[22,10]],[[1,6],[5,9],[11,7],[12,10],[14,8],[15,4],[17,19],[18,16],[20,13],[21,2],[22,3]],[[1,7],[5,0],[11,10],[12,9],[14,16],[15,2],[17,13],[18,8],[20,3],[21,19],[22,6]],[[1,8],[5,10],[11,0],[12,19],[14,9],[15,16],[17,3],[18,6],[20,4],[21,7],[22,2]],[[1,9],[5,13],[11,19],[12,0],[14,2],[15,6],[17,4],[18,7],[20,16],[21,3],[22,8]],[[1,19],[5,3],[11,16],[12,2],[14,13],[15,0],[17,6],[18,9],[20,8],[21,10],[22,4]]],
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[[[0,1],[2,17],[5,4],[7,3],[11,18],[13,8],[14,12],[15,22],[16,21],[19,9],[20,10]],[[0,3],[2,21],[5,8],[7,1],[11,9],[13,10],[14,6],[15,4],[16,12],[19,22],[20,17]],[[0,4],[2,12],[5,1],[7,18],[11,3],[13,17],[14,9],[15,21],[16,22],[19,10],[20,6]],[[0,8],[2,3],[5,18],[7,6],[11,4],[13,12],[14,10],[15,9],[16,17],[19,21],[20,1]],[[0,17],[2,6],[5,10],[7,21],[11,1],[13,9],[14,18],[15,3],[16,4],[19,8],[20,22]],[[0,18],[2,1],[5,12],[7,22],[11,21],[13,3],[14,17],[15,6],[16,10],[19,4],[20,8]],[[0,22],[2,8],[5,6],[7,10],[11,12],[13,4],[14,21],[15,17],[16,1],[19,18],[20,9]]],
[[[2,1],[3,7],[5,10],[8,19],[11,9],[12,14],[13,6],[15,4],[17,0],[18,16],[20,22]],[[2,7],[3,4],[5,1],[8,14],[11,6],[12,21],[13,19],[15,22],[17,16],[18,9],[20,0]],[[2,9],[3,21],[5,7],[8,16],[11,4],[12,0],[13,22],[15,10],[17,19],[18,14],[20,1]],[[2,10],[3,14],[5,6],[8,1],[11,19],[12,22],[13,16],[15,0],[17,7],[18,4],[20,21]],[[2,16],[3,10],[5,0],[8,21],[11,14],[12,19],[13,7],[15,1],[17,4],[18,6],[20,9]],[[2,19],[3,9],[5,14],[8,10],[11,0],[12,7],[13,21],[15,6],[17,1],[18,22],[20,4]],[[2,22],[3,16],[5,9],[8,6],[11,21],[12,10],[13,4],[15,19],[17,14],[18,1],[20,7]]],
[[[0,1],[3,13],[4,15],[7,12],[8,18],[11,17],[14,6],[16,10],[19,20],[21,9],[22,2]],[[0,2],[3,1],[4,10],[7,6],[8,17],[11,5],[14,18],[16,12],[19,13],[21,15],[22,9]],[[0,5],[3,6],[4,2],[7,1],[8,15],[11,12],[14,20],[16,18],[19,17],[21,13],[22,10]],[[0,6],[3,18],[4,17],[7,20],[8,5],[11,2],[14,10],[16,13],[19,9],[21,1],[22,15]],[[0,12],[3,17],[4,6],[7,9],[8,2],[11,10],[14,1],[16,15],[19,18],[21,20],[22,5]],[[0,13],[3,9],[4,12],[7,2],[8,20],[11,1],[14,15],[16,5],[19,10],[21,17],[22,18]],[[0,15],[3,5],[4,20],[7,18],[8,1],[11,9],[14,13],[16,17],[19,2],[21,12],[22,6]]],
[[[0,4],[1,14],[6,16],[9,5],[11,3],[12,10],[13,22],[17,7],[19,8],[20,15],[21,18]],[[0,5],[1,4],[6,22],[9,8],[11,2],[12,15],[13,7],[17,3],[19,18],[20,16],[21,10]],[[0,7],[1,10],[6,8],[9,16],[11,14],[12,3],[13,5],[17,2],[19,22],[20,18],[21,15]],[[0,10],[1,5],[6,3],[9,4],[11,22],[12,18],[13,16],[17,15],[19,14],[20,2],[21,7]],[[0,16],[1,2],[6,4],[9,18],[11,7],[12,22],[13,15],[17,14],[19,3],[20,10],[21,8]],[[0,18],[1,16],[6,10],[9,15],[11,5],[12,4],[13,2],[17,8],[19,7],[20,3],[21,14]],[[0,22],[1,15],[6,2],[9,3],[11,10],[12,14],[13,8],[17,4],[19,16],[20,7],[21,5]]],
[[[0,2],[1,11],[5,19],[7,22],[8,6],[10,4],[13,15],[14,9],[16,18],[20,12],[21,17]],[[0,3],[1,18],[5,6],[7,19],[8,9],[10,15],[13,4],[14,11],[16,2],[20,17],[21,22]],[[0,9],[1,15],[5,3],[7,2],[8,18],[10,19],[13,12],[14,22],[16,4],[20,11],[21,6]],[[0,12],[1,17],[5,11],[7,6],[8,4],[10,3],[13,18],[14,2],[16,15],[20,19],[21,9]],[[0,15],[1,6],[5,4],[7,12],[8,17],[10,11],[13,19],[14,18],[16,22],[20,9],[21,3]],[[0,17],[1,22],[5,18],[7,15],[8,2],[10,9],[13,6],[14,12],[16,19],[20,3],[21,4]],[[0,18],[1,12],[5,22],[7,3],[8,11],[10,2],[13,9],[14,19],[16,17],[20,6],[21,15]]],
[[[2,3],[4,9],[7,21],[10,17],[11,6],[12,19],[13,1],[15,14],[16,0],[18,5],[20,22]],[[2,5],[4,17],[7,3],[10,21],[11,1],[12,6],[13,22],[15,8],[16,14],[18,9],[20,0]],[[2,8],[4,1],[7,14],[10,3],[11,19],[12,9],[13,17],[15,5],[16,6],[18,22],[20,21]],[[2,9],[4,5],[7,17],[10,19],[11,0],[12,22],[13,6],[15,1],[16,8],[18,21],[20,3]],[[2,17],[4,14],[7,6],[10,1],[11,8],[12,5],[13,21],[15,3],[16,9],[18,0],[20,19]],[[2,19],[4,8],[7,5],[10,9],[11,17],[12,21],[13,0],[15,22],[16,3],[18,14],[20,6]],[[2,22],[4,21],[7,19],[10,0],[11,5],[12,1],[13,14],[15,6],[16,17],[18,3],[20,8]]],
[[[0,1],[3,22],[4,6],[5,14],[9,15],[10,8],[13,16],[17,11],[18,12],[20,19],[21,2]],[[0,6],[3,15],[4,19],[5,7],[9,22],[10,11],[13,12],[17,2],[18,8],[20,1],[21,16]],[[0,7],[3,12],[4,2],[5,1],[9,16],[10,15],[13,14],[17,22],[18,6],[20,11],[21,19]],[[0,8],[3,19],[4,16],[5,2],[9,11],[10,7],[13,22],[17,1],[18,15],[20,6],[21,14]],[[0,12],[3,2],[4,11],[5,8],[9,19],[10,6],[13,1],[17,14],[18,16],[20,7],[21,15]],[[0,16],[3,7],[4,1],[5,12],[9,6],[10,2],[13,19],[17,8],[18,14],[20,22],[21,11]],[[0,22],[3,6],[4,12],[5,19],[9,8],[10,1],[13,15],[17,16],[18,2],[20,14],[21,7]]],
[[[1,0],[2,4],[5,9],[8,11],[10,13],[12,17],[16,22],[18,7],[19,3],[20,6],[21,15]],[[1,3],[2,11],[5,7],[8,17],[10,9],[12,15],[16,0],[18,6],[19,14],[20,13],[21,22]],[[1,4],[2,22],[5,3],[8,13],[10,6],[12,7],[16,14],[18,15],[19,11],[20,9],[21,17]],[[1,9],[2,15],[5,17],[8,22],[10,11],[12,13],[16,7],[18,14],[19,0],[20,4],[21,6]],[[1,13],[2,6],[5,0],[8,3],[10,17],[12,22],[16,9],[18,11],[19,15],[20,14],[21,4]],[[1,14],[2,13],[5,4],[8,6],[10,15],[12,0],[16,11],[18,3],[19,17],[20,7],[21,9]],[[1,15],[2,14],[5,11],[8,7],[10,0],[12,4],[16,13],[18,9],[19,22],[20,17],[21,3]]],
[[[0,6],[2,17],[5,9],[7,3],[8,1],[12,16],[14,10],[18,11],[19,15],[21,20],[22,4]],[[0,9],[2,16],[5,6],[7,10],[8,15],[12,3],[14,4],[18,13],[19,1],[21,17],[22,20]],[[0,10],[2,9],[5,11],[7,20],[8,16],[12,1],[14,6],[18,3],[19,17],[21,13],[22,15]],[[0,11],[2,1],[5,20],[7,13],[8,4],[12,6],[14,17],[18,15],[19,10],[21,16],[22,9]],[[0,13],[2,20],[5,4],[7,1],[8,6],[12,15],[14,11],[18,17],[19,16],[21,3],[22,10]],[[0,15],[2,4],[5,1],[7,9],[8,17],[12,10],[14,3],[18,20],[19,11],[21,6],[22,13]],[[0,17],[2,3],[5,15],[7,11],[8,13],[12,9],[14,1],[18,4],[19,20],[21,10],[22,16]]],
[[[1,6],[2,17],[4,11],[5,12],[8,0],[13,3],[14,21],[15,7],[18,10],[19,16],[20,9]],[[1,7],[2,0],[4,9],[5,17],[8,12],[13,6],[14,3],[15,21],[18,22],[19,11],[20,16]],[[1,9],[2,16],[4,22],[5,3],[8,21],[13,12],[14,6],[15,11],[18,17],[19,10],[20,7]],[[1,11],[2,7],[4,6],[5,22],[8,9],[13,0],[14,12],[15,10],[18,16],[19,3],[20,17]],[[1,16],[2,21],[4,12],[5,0],[8,11],[13,7],[14,22],[15,17],[18,3],[19,6],[20,10]],[[1,17],[2,3],[4,10],[5,6],[8,22],[13,21],[14,11],[15,12],[18,9],[19,7],[20,0]],[[1,21],[2,22],[4,7],[5,10],[8,17],[13,9],[14,16],[15,3],[18,11],[19,0],[20,12]]],
[[[2,0],[4,5],[9,7],[11,12],[13,17],[15,10],[16,8],[19,18],[20,14],[21,1],[22,3]],[[2,3],[4,12],[9,6],[11,5],[13,10],[15,14],[16,7],[19,0],[20,8],[21,18],[22,17]],[[2,5],[4,18],[9,10],[11,8],[13,14],[15,12],[16,3],[19,1],[20,6],[21,17],[22,0]],[[2,6],[4,10],[9,0],[11,14],[13,18],[15,8],[16,1],[19,3],[20,7],[21,5],[22,12]],[[2,7],[4,1],[9,5],[11,18],[13,3],[15,17],[16,10],[19,14],[20,12],[21,0],[22,6]],[[2,8],[4,6],[9,14],[11,17],[13,0],[15,1],[16,5],[19,12],[20,3],[21,7],[22,10]],[[2,18],[4,8],[9,1],[11,3],[13,7],[15,0],[16,17],[19,6],[20,10],[21,12],[22,5]]],
[[[0,5],[1,3],[2,20],[6,17],[10,4],[11,14],[15,12],[16,13],[18,22],[19,9],[21,8]],[[0,7],[1,17],[2,12],[6,4],[10,8],[11,9],[15,5],[16,22],[18,20],[19,13],[21,3]],[[0,8],[1,7],[2,17],[6,13],[10,12],[11,3],[15,14],[16,4],[18,9],[19,20],[21,22]],[[0,14],[1,12],[2,5],[6,20],[10,9],[11,22],[15,13],[16,3],[18,17],[19,7],[21,4]],[[0,17],[1,22],[2,3],[6,7],[10,13],[11,4],[15,20],[16,14],[18,5],[19,8],[21,12]],[[0,20],[1,14],[2,13],[6,9],[10,17],[11,8],[15,4],[16,5],[18,12],[19,22],[21,7]],[[0,22],[1,9],[2,7],[6,14],[10,3],[11,20],[15,8],[16,17],[18,4],[19,12],[21,5]]],
[[[1,0],[2,9],[6,15],[10,16],[13,19],[14,7],[17,3],[18,8],[20,11],[21,5],[22,4]],[[1,7],[2,8],[6,11],[10,4],[13,15],[14,12],[17,9],[18,16],[20,3],[21,0],[22,19]],[[1,9],[2,16],[6,12],[10,19],[13,11],[14,15],[17,7],[18,3],[20,5],[21,8],[22,0]],[[1,11],[2,3],[6,8],[10,12],[13,4],[14,5],[17,0],[18,15],[20,7],[21,16],[22,9]],[[1,12],[2,7],[6,0],[10,15],[13,5],[14,3],[17,4],[18,9],[20,8],[21,19],[22,16]],[[1,15],[2,12],[6,4],[10,7],[13,16],[14,0],[17,11],[18,5],[20,19],[21,9],[22,3]],[[1,19],[2,11],[6,3],[10,8],[13,0],[14,16],[17,5],[18,4],[20,15],[21,7],[22,12]]],
[[[3,1],[6,20],[7,5],[8,0],[10,16],[12,11],[13,2],[18,9],[19,14],[21,15],[22,17]],[[3,2],[6,15],[7,1],[8,11],[10,5],[12,14],[13,16],[18,17],[19,4],[21,0],[22,9]],[[3,4],[6,11],[7,16],[8,5],[10,15],[12,9],[13,20],[18,1],[19,17],[21,2],[22,0]],[[3,9],[6,4],[7,0],[8,15],[10,1],[12,17],[13,14],[18,20],[19,2],[21,11],[22,5]],[[3,16],[6,5],[7,11],[8,2],[10,14],[12,4],[13,17],[18,0],[19,20],[21,1],[22,15]],[[3,17],[6,9],[7,20],[8,14],[10,2],[12,16],[13,15],[18,11],[19,5],[21,4],[22,1]],[[3,20],[6,1],[7,2],[8,9],[10,4],[12,15],[13,0],[18,14],[19,11],[21,17],[22,16]]],
[[[1,4],[2,22],[3,10],[7,12],[13,5],[14,6],[15,9],[16,11],[17,8],[19,21],[20,0]],[[1,5],[2,12],[3,11],[7,4],[13,6],[14,22],[15,10],[16,18],[17,0],[19,9],[20,8]],[[1,6],[2,21],[3,9],[7,10],[13,0],[14,8],[15,12],[16,5],[17,22],[19,4],[20,18]],[[1,8],[2,4],[3,21],[7,6],[13,22],[14,10],[15,0],[16,9],[17,11],[19,18],[20,5]],[[1,10],[2,18],[3,6],[7,11],[13,9],[14,0],[15,5],[16,12],[17,21],[19,8],[20,4]],[[1,12],[2,0],[3,8],[7,22],[13,4],[14,18],[15,21],[16,6],[17,9],[19,10],[20,11]],[[1,18],[2,6],[3,5],[7,9],[13,8],[14,11],[15,4],[16,0],[17,12],[19,22],[20,21]]],
[[[0,5],[2,19],[3,22],[4,11],[6,1],[7,18],[12,20],[14,17],[15,9],[16,13],[21,10]],[[0,9],[2,18],[3,10],[4,13],[6,20],[7,5],[12,1],[14,22],[15,8],[16,17],[21,11]],[[0,10],[2,13],[3,5],[4,17],[6,8],[7,9],[12,11],[14,18],[15,19],[16,20],[21,1]],[[0,11],[2,20],[3,13],[4,1],[6,17],[7,22],[12,19],[14,10],[15,5],[16,9],[21,8]],[[0,19],[2,17],[3,8],[4,9],[6,22],[7,11],[12,13],[14,1],[15,10],[16,5],[21,18]],[[0,20],[2,9],[3,18],[4,22],[6,10],[7,1],[12,5],[14,19],[15,13],[16,8],[21,17]],[[0,22],[2,10],[3,20],[4,19],[6,9],[7,8],[12,18],[14,5],[15,1],[16,11],[21,13]]],
[[[0,5],[2,10],[3,1],[6,12],[7,11],[8,14],[15,17],[16,9],[18,13],[20,19],[22,4]],[[0,9],[2,12],[3,21],[6,13],[7,1],[8,5],[15,4],[16,19],[18,11],[20,10],[22,17]],[[0,12],[2,1],[3,5],[6,4],[7,19],[8,17],[15,21],[16,10],[18,9],[20,14],[22,13]],[[0,13],[2,17],[3,10],[6,11],[7,5],[8,21],[15,14],[16,12],[18,4],[20,9],[22,19]],[[0,14],[2,5],[3,13],[6,21],[7,4],[8,9],[15,19],[16,11],[18,10],[20,12],[22,1]],[[0,17],[2,11],[3,12],[6,5],[7,10],[8,1],[15,13],[16,21],[18,14],[20,4],[22,9]],[[0,19],[2,9],[3,14],[6,17],[7,21],[8,4],[15,10],[16,13],[18,5],[20,1],[22,11]]],
[[[0,1],[3,14],[4,6],[8,16],[9,7],[10,20],[12,5],[13,17],[15,18],[19,11],[21,2]],[[0,2],[3,18],[4,22],[8,17],[9,5],[10,6],[12,14],[13,1],[15,20],[19,7],[21,11]],[[0,5],[3,20],[4,17],[8,11],[9,2],[10,18],[12,16],[13,7],[15,14],[19,22],[21,1]],[[0,7],[3,6],[4,1],[8,2],[9,17],[10,5],[12,20],[13,16],[15,22],[19,14],[21,18]],[[0,11],[3,2],[4,7],[8,22],[9,14],[10,17],[12,6],[13,20],[15,16],[19,1],[21,5]],[[0,16],[3,17],[4,5],[8,14],[9,18],[10,7],[12,1],[13,22],[15,11],[19,20],[21,6]],[[0,20],[3,22],[4,2],[8,1],[9,16],[10,11],[12,17],[13,18],[15,5],[19,6],[21,14]]],
[[[1,0],[2,13],[3,20],[4,10],[5,19],[8,16],[9,21],[11,15],[14,6],[17,12],[22,18]],[[1,7],[2,12],[3,15],[4,18],[5,21],[8,13],[9,10],[11,6],[14,20],[17,19],[22,16]],[[1,10],[2,18],[3,19],[4,7],[5,0],[8,15],[9,20],[11,13],[14,21],[17,16],[22,6]],[[1,13],[2,0],[3,12],[4,20],[5,10],[8,21],[9,15],[11,7],[14,16],[17,6],[22,19]],[[1,15],[2,19],[3,10],[4,13],[5,18],[8,20],[9,7],[11,16],[14,0],[17,21],[22,12]],[[1,16],[2,7],[3,0],[4,21],[5,13],[8,19],[9,6],[11,12],[14,18],[17,15],[22,20]],[[1,21],[2,16],[3,13],[4,12],[5,6],[8,18],[9,19],[11,20],[14,7],[17,0],[22,10]]],
[[[4,0],[5,1],[6,20],[10,22],[11,15],[12,2],[13,16],[14,7],[17,21],[18,9],[19,3]],[[4,1],[5,9],[6,16],[10,8],[11,0],[12,21],[13,3],[14,15],[17,7],[18,22],[19,2]],[[4,7],[5,21],[6,15],[10,9],[11,16],[12,8],[13,22],[14,20],[17,2],[18,0],[19,1]],[[4,9],[5,7],[6,1],[10,15],[11,21],[12,20],[13,8],[14,16],[17,3],[18,2],[19,0]],[[4,20],[5,2],[6,21],[10,0],[11,3],[12,15],[13,1],[14,9],[17,22],[18,8],[19,16]],[[4,21],[5,15],[6,22],[10,3],[11,20],[12,7],[13,9],[14,1],[17,0],[18,16],[19,8]],[[4,22],[5,3],[6,2],[10,7],[11,9],[12,0],[13,21],[14,8],[17,16],[18,20],[19,15]]],
[[[2,1],[3,16],[4,20],[5,22],[9,17],[10,14],[12,0],[13,18],[15,7],[19,11],[21,6]],[[2,8],[3,11],[4,16],[5,17],[9,18],[10,6],[12,1],[13,22],[15,0],[19,14],[21,20]],[[2,11],[3,6],[4,17],[5,0],[9,1],[10,18],[12,16],[13,20],[15,8],[19,22],[21,7]],[[2,14],[3,20],[4,22],[5,8],[9,0],[10,11],[12,6],[13,7],[15,16],[19,1],[21,18]],[[2,16],[3,1],[4,11],[5,20],[9,14],[10,8],[12,22],[13,17],[15,18],[19,7],[21,0]],[[2,17],[3,8],[4,0],[5,14],[9,20],[10,22],[12,7],[13,1],[15,11],[19,6],[21,16]],[[2,22],[3,18],[4,6],[5,7],[9,11],[10,0],[12,8],[13,16],[15,17],[19,20],[21,14]]],
[[[0,3],[2,1],[4,17],[5,16],[9,11],[12,7],[13,14],[15,19],[20,18],[21,10],[22,8]],[[0,6],[2,3],[4,14],[5,10],[9,7],[12,18],[13,11],[15,8],[20,1],[21,19],[22,16]],[[0,7],[2,11],[4,1],[5,8],[9,17],[12,10],[13,19],[15,3],[20,6],[21,16],[22,18]],[[0,10],[2,7],[4,6],[5,17],[9,19],[12,11],[13,16],[15,18],[20,3],[21,8],[22,14]],[[0,11],[2,19],[4,10],[5,7],[9,8],[12,1],[13,17],[15,6],[20,16],[21,14],[22,3]],[[0,16],[2,18],[4,11],[5,3],[9,10],[12,14],[13,6],[15,17],[20,8],[21,1],[22,19]],[[0,19],[2,17],[4,3],[5,1],[9,14],[12,16],[13,18],[15,10],[20,11],[21,6],[22,7]]],
[[[0,2],[5,3],[7,15],[8,21],[9,4],[10,1],[11,6],[13,12],[14,19],[16,22],[20,17]],[[0,4],[5,12],[7,3],[8,2],[9,6],[10,19],[11,1],[13,17],[14,22],[16,18],[20,21]],[[0,6],[5,17],[7,2],[8,1],[9,22],[10,21],[11,12],[13,19],[14,4],[16,15],[20,18]],[[0,12],[5,4],[7,22],[8,6],[9,15],[10,18],[11,17],[13,3],[14,21],[16,19],[20,1]],[[0,18],[5,1],[7,6],[8,12],[9,21],[10,2],[11,15],[13,22],[14,3],[16,17],[20,19]],[[0,21],[5,15],[7,19],[8,17],[9,3],[10,12],[11,22],[13,18],[14,2],[16,4],[20,6]],[[0,22],[5,19],[7,12],[8,3],[9,17],[10,15],[11,18],[13,21],[14,1],[16,2],[20,4]]], 
# next fifty random ancilla preparation circuits
[[[2,1],[5,0],[6,14],[7,22],[8,12],[9,11],[13,3],[15,4],[16,18],[17,10],[20,19]],[[2,3],[5,1],[6,0],[7,14],[8,19],[9,21],[13,4],[15,22],[16,11],[17,12],[20,18]],[[2,4],[5,22],[6,18],[7,12],[8,3],[9,1],[13,0],[15,10],[16,19],[17,11],[20,21]],[[2,14],[5,12],[6,19],[7,10],[8,22],[9,3],[13,21],[15,18],[16,1],[17,4],[20,11]],[[2,19],[5,14],[6,3],[7,21],[8,1],[9,4],[13,11],[15,12],[16,22],[17,0],[20,10]],[[2,21],[5,11],[6,1],[7,19],[8,10],[9,12],[13,22],[15,14],[16,0],[17,18],[20,3]],[[2,22],[5,4],[6,12],[7,0],[8,11],[9,18],[13,10],[15,3],[16,21],[17,19],[20,14]]],
[[[0,2],[1,21],[3,18],[4,20],[5,22],[7,8],[10,19],[13,9],[14,11],[15,6],[17,16]],[[0,8],[1,20],[3,9],[4,12],[5,2],[7,18],[10,22],[13,6],[14,19],[15,16],[17,11]],[[0,9],[1,19],[3,16],[4,8],[5,6],[7,21],[10,20],[13,11],[14,18],[15,22],[17,12]],[[0,16],[1,8],[3,2],[4,6],[5,11],[7,12],[10,18],[13,21],[14,9],[15,19],[17,20]],[[0,18],[1,9],[3,21],[4,16],[5,12],[7,19],[10,6],[13,20],[14,22],[15,11],[17,2]],[[0,20],[1,11],[3,19],[4,21],[5,8],[7,6],[10,12],[13,22],[14,2],[15,9],[17,18]],[[0,22],[1,2],[3,6],[4,9],[5,20],[7,11],[10,16],[13,18],[14,12],[15,8],[17,21]]],
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[[[0,4],[2,21],[3,16],[6,18],[9,5],[10,14],[11,15],[12,19],[13,1],[17,8],[20,22]],[[0,8],[2,16],[3,19],[6,15],[9,7],[10,18],[11,1],[12,21],[13,5],[17,22],[20,4]],[[0,14],[2,4],[3,22],[6,1],[9,15],[10,8],[11,19],[12,5],[13,18],[17,7],[20,16]],[[0,15],[2,7],[3,18],[6,19],[9,22],[10,21],[11,14],[12,16],[13,4],[17,1],[20,8]],[[0,16],[2,1],[3,8],[6,7],[9,4],[10,5],[11,18],[12,14],[13,15],[17,21],[20,19]],[[0,21],[2,18],[3,14],[6,5],[9,19],[10,7],[11,8],[12,4],[13,22],[17,15],[20,1]],[[0,22],[2,8],[3,7],[6,16],[9,14],[10,15],[11,4],[12,18],[13,21],[17,19],[20,5]]],
[[[0,3],[1,22],[4,10],[5,8],[7,18],[9,16],[12,13],[14,15],[17,19],[20,2],[21,11]],[[0,6],[1,13],[4,22],[5,16],[7,11],[9,15],[12,18],[14,8],[17,10],[20,3],[21,2]],[[0,13],[1,8],[4,16],[5,10],[7,22],[9,11],[12,6],[14,3],[17,18],[20,19],[21,15]],[[0,15],[1,19],[4,2],[5,18],[7,10],[9,8],[12,11],[14,13],[17,6],[20,22],[21,3]],[[0,16],[1,18],[4,6],[5,11],[7,19],[9,22],[12,2],[14,10],[17,3],[20,13],[21,8]],[[0,18],[1,2],[4,3],[5,19],[7,15],[9,6],[12,10],[14,11],[17,8],[20,16],[21,22]],[[0,22],[1,6],[4,8],[5,2],[7,13],[9,19],[12,3],[14,16],[17,15],[20,11],[21,18]]],
[[[0,2],[1,9],[7,21],[8,18],[10,3],[13,17],[14,4],[15,12],[16,20],[19,6],[22,5]],[[0,5],[1,4],[7,6],[8,2],[10,21],[13,11],[14,9],[15,3],[16,17],[19,12],[22,20]],[[0,6],[1,11],[7,3],[8,4],[10,18],[13,12],[14,2],[15,5],[16,21],[19,20],[22,17]],[[0,9],[1,21],[7,11],[8,17],[10,4],[13,5],[14,6],[15,18],[16,2],[19,3],[22,12]],[[0,17],[1,12],[7,20],[8,6],[10,5],[13,4],[14,3],[15,21],[16,18],[19,11],[22,9]],[[0,20],[1,3],[7,4],[8,9],[10,2],[13,21],[14,12],[15,6],[16,11],[19,17],[22,18]],[[0,21],[1,18],[7,2],[8,11],[10,17],[13,6],[14,5],[15,20],[16,12],[19,9],[22,4]]],
[[[0,1],[2,22],[4,3],[5,6],[7,20],[8,16],[9,18],[10,14],[15,12],[19,17],[21,11]],[[0,3],[2,14],[4,6],[5,16],[7,17],[8,18],[9,13],[10,20],[15,1],[19,11],[21,12]],[[0,11],[2,6],[4,13],[5,17],[7,1],[8,20],[9,3],[10,12],[15,22],[19,14],[21,16]],[[0,12],[2,3],[4,1],[5,20],[7,13],[8,11],[9,16],[10,22],[15,17],[19,18],[21,6]],[[0,13],[2,17],[4,22],[5,12],[7,18],[8,1],[9,20],[10,11],[15,6],[19,16],[21,14]],[[0,16],[2,18],[4,20],[5,14],[7,22],[8,6],[9,12],[10,17],[15,11],[19,13],[21,3]],[[0,17],[2,20],[4,12],[5,1],[7,16],[8,3],[9,14],[10,13],[15,18],[19,6],[21,22]]]
]


def prepCircuits():
	return preparationCircuits

def randomAncillaZPrep(i, roundPerm, name):
	return ancillaZPrep(preparationCircuits[i], roundPerm, name)




def permuteCircuit(circuit, rounds):
	return [circuit[r] for r in rounds]

def ancillaZPrep(schedule, roundPermutation, name='0'):
	"""Returns the location list for the input list of CNOTs (in seven rounds)."""
	
	warn('Use qec.encode.ancilla.ancillaZPrep(), instead.', DeprecationWarning)
	
	cnots = permuteCircuit(schedule, roundPermutation)
	
	locations = []
	def addLoc(loc):
		locations.append(loc)

	flatcnots = reduce(lambda x,y: x+y, cnots)
	
	# A qubit that is a target of any CNOT in the prep circuit should
	# be prepared as |0>.  All other qubits should be prepared as |+>
	prepAsZ  = set([c[1] for c in flatcnots])
	prepAsX = set(range(23)) - prepAsZ 

	# the initial preparations |+>^{11}|0>^{12} (up to some permutation)
	for i in prepAsX:
		addLoc(locXprep(name, i))
	for i in prepAsZ:
		addLoc(locZprep(name, i))

	touched = set()
	
	for rnd in range(7):			# simulate each of the seven rounds sequentially
		resting = set(touched)
		for src, tgt in cnots[rnd]:
			cnotQubits = set([src, tgt])
			addLoc(loccnot(name, src, name, tgt))
			resting -= cnotQubits
			touched.update(cnotQubits)
			
		# now add the rest locations, provided we are in at least the second round
		for r in resting:
			addLoc(locrest(name, r))
			
	propagateAllErrors(locations)
	return locations

def getOverlapPreps(includeRests=True):

	perms = overlap.bestXZset
	cnotsA0 = overlap.getOverlapPrep(perms[0][0])
	cnotsA1 = overlap.getOverlapPrep(perms[0][1])
	cnotsA2 = overlap.getOverlapPrep(perms[1][0])
	cnotsA3 = overlap.getOverlapPrep(perms[1][1])
	
	zeroPrepA0 = Locations(ancillaZPrep(cnotsA0, range(7), 'A'), 'OverlapGolay0.A0')
	zeroPrepA1 = Locations(ancillaZPrep(cnotsA1, range(7), 'B'), 'OverlapGolay0.A1')
	zeroPrepA2 = Locations(ancillaZPrep(cnotsA2, range(7), 'A'), 'OverlapGolay0.A2')
	zeroPrepA3 = Locations(ancillaZPrep(cnotsA3, range(7), 'B'), 'OverlapGolay0.A3')
	
	
	if not includeRests:
		zeroPrepA0 = zeroPrepA0.filterAgainst('rest')
		zeroPrepA1 = zeroPrepA1.filterAgainst('rest')
		zeroPrepA2 = zeroPrepA2.filterAgainst('rest')
		zeroPrepA3 = zeroPrepA3.filterAgainst('rest')

	return zeroPrepA0, zeroPrepA1, zeroPrepA2, zeroPrepA3


goodRandomPreps = [
		[[8, 70, [0, 6, 2, 4, 1, 3, 5], [1, 4, 5, 6, 0, 3, 2]],  [45, 99, [6, 5, 1, 3, 2, 4, 0], [0, 5, 1, 3, 6, 4, 2]]],
		[[29, 44, [0, 5, 4, 6, 2, 3, 1], [3, 1, 0, 2, 5, 6, 4]], [76, 99, [6, 2, 5, 0, 1, 4, 3], [2, 1, 6, 0, 3, 4, 5]]],
		[[30, 59, [4, 2, 3, 5, 6, 0, 1], [3, 2, 6, 1, 4, 0, 5]], [63, 80, [3, 6, 0, 4, 1, 2, 5], [3, 0, 6, 5, 4, 1, 2]]],
		[[30, 59, [4, 2, 3, 5, 6, 0, 1], [3, 2, 6, 1, 4, 0, 5]], [76, 99, [6, 2, 5, 0, 1, 4, 3], [2, 1, 6, 0, 3, 4, 5]]],
		[[45, 99, [6, 5, 1, 3, 2, 4, 0], [0, 5, 1, 3, 6, 4, 2]], [90, 91, [3, 5, 2, 4, 0, 6, 1], [5, 6, 4, 1, 3, 0, 2]]],
		[[76, 99, [6, 2, 5, 0, 1, 4, 3], [2, 1, 6, 0, 3, 4, 5]], [90, 91, [3, 5, 2, 4, 0, 6, 1], [5, 6, 4, 1, 3, 0, 2]]]
	]

def getSteaneRandomPreps(includeRests=True, index=0):
	prep = goodRandomPreps[index]
	pair1, pair2 = prep
	
	def labelStr(index, perm):
		return 'Golay0.{0}.{1}'.format(index, perm).replace(',','')
	
	zeroPrep1 = randomAncillaZPrep(pair1[0], pair1[2], 'A')
	zeroPrep1 = Locations(zeroPrep1, labelStr(pair1[0], pair1[2]))
	
	zeroPrep2 = randomAncillaZPrep(pair1[1], pair1[3], 'B')
	zeroPrep2 = Locations(zeroPrep2, labelStr(pair1[1], pair1[3]))
	
	zeroPrep3 = randomAncillaZPrep(pair2[0], pair2[2], 'A')
	zeroPrep3 = Locations(zeroPrep3, labelStr(pair2[0], pair2[2]))
	
	zeroPrep4 = randomAncillaZPrep(pair2[1], pair2[3], 'B')
	zeroPrep4 = Locations(zeroPrep4, labelStr(pair2[1], pair2[3]))
	
	if not includeRests:
		zeroPrep1 = zeroPrep1.filterAgainst('rest')
		zeroPrep2 = zeroPrep2.filterAgainst('rest')
		zeroPrep3 = zeroPrep3.filterAgainst('rest')
		zeroPrep4 = zeroPrep4.filterAgainst('rest')

	return zeroPrep1, zeroPrep2, zeroPrep3, zeroPrep4